Combining an OpenFOAM\(^{\textregistered }\)-Based Adjoint Solver with RBF Morphing for Shape Optimization Problems on the RBF4AERO Platform

  • E. M. Papoutsis-KiachagiasEmail author
  • K. C. Giannakoglou
  • S. Porziani
  • C. Groth
  • M. E. Biancolini
  • E. Costa
  • M. Andrejašič


This chapter presents a combination of an OpenFOAM\(^{\textregistered }\)-based continuous adjoint solver and a Radial Basis Function (RBF)-based morpher forming a software suite able to tackle shape optimization problems. The adjoint method provides a fast and accurate way for computing the sensitivity derivatives of the objective functions (here, drag and lift forces) with respect to the design variables. The latter control a group of RBF control points used to deform both the surface and volume mesh of the CFD domain. The use of the RBF-based morpher provides a fast and robust way of handling mesh and geometry deformations with the same tool. The coupling of the above-mentioned tools is used to tackle shape optimization problems in automotive and aerospace engineering. This work was funded by the RBF4AERO “Innovative benchmark technology for aircraft engineering design and efficient design phase optimisation” project funded by the EU 7th Framework Programme (FP7-AAT, 2007-2013) under Grant Agreement No. 605396 and the presented methods are available for use through the RBF4AERO platform (



Radial basis functions


Sensitivity derivatives


Finite differences


Partial differential equation


Surface integrals


Field integrals


Enhanced surface integrals


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • E. M. Papoutsis-Kiachagias
    • 1
    Email author
  • K. C. Giannakoglou
    • 1
  • S. Porziani
    • 2
  • C. Groth
    • 3
  • M. E. Biancolini
    • 3
  • E. Costa
    • 2
  • M. Andrejašič
    • 4
  1. 1.Parallel CFD & Optimization UnitNational Technical University of Athens (NTUA)AthensGreece
  2. 2.D’Appolonia S.p.A.RomeItaly
  3. 3.University of Rome Tor Vergata (UTV)RomeItaly
  4. 4.PIPISTREL d.o.o. Ajdovščina, R&D, Department of AerodynamicsAjdovščinaSlovenia

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